Millán Ana P, Sun Hanlin, Torres Joaquín J, Bianconi Ginestra
Electromagnetism and Matter Physics Department, Institute "Carlos I" for Theoretical and Computational Physics, University of Granada, Granada E-18071, Spain.
Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm SE-106 91, Sweden.
PNAS Nexus. 2024 Jul 9;3(7):pgae270. doi: 10.1093/pnasnexus/pgae270. eCollection 2024 Jul.
Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here, we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns, and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time dependent as in neuroscience.
三元相互作用是一种高阶相互作用，当一组节点影响另外两个节点之间的相互作用时就会发生。当胶质细胞调节神经元对之间的突触信号时，或者当中间神经元轴突-轴突突触实现突触前抑制和易化时，大脑中就存在三元相互作用的例子；在生态系统中，当一个或多个物种能够影响另外两个物种之间的相互作用时，也存在三元相互作用的例子。在随机图上，最近已表明三元渗流会将渗流转变为一个成熟的动力学过程，其中巨分量的大小经历一条通向混沌的路径。然而，在许多实际情况中，三元相互作用是局部的，并且发生在空间嵌入网络上。在这里，我们表明空间网络中的三元相互作用会对巨分量产生非常复杂的时空调制，从而产生具有显著不同拓扑结构的三元渗流模式。我们用拓扑数据分析对观察到的模式（条纹、章鱼和小簇）进行分类，并评估它们的信息含量（熵和复杂度）。此外，我们说明了三元渗流模式动力学的多稳定性，并提供了该模型的全面相图。这些结果为渗流开辟了新的视角，因为它们表明在存在空间三元相互作用的情况下，巨分量可以获得随时间变化的拓扑结构。因此，这项工作提供了一个理论框架，可应用于对现实场景进行建模，在这些场景中，如在神经科学中一样，巨分量是随时间变化的。
